[PDF] Cyclonic and anticyclonic contributions to atmospheric energetics

14390_3Okajima_Nakamura_Kaspi_2021.pdf | (2021) 11:13202 | www.nature.com/scientificreports *

Transient cyclones and anticyclones are a fundamental component of the extratropical climate system, caus

-

ing day-to-day weather variations. By systematically transporting heat and westerly momentum, they also act

to maintain the meridional thermal structure and a midlatitude westerly jet stream in each hemisphere. ?eir

occurrence and intensities are thus very important to climate dynamics1,2 and regional extreme weather events 3-6 ,

and therefore further investigating their behavior under the current and future climatic conditions is of great

scienti?c and societal importance.

Since the late nineteenth

century 7 , investigation of transient eddies, especially extratropical cyclones, has relied on a "Lagrangian approach", which tracks individual moving cyclones or anticyclones 8-10 . Since gridded

atmospheric datasets (analyses) became available 45 years ago, however, an "Eulerian approach" has become used

widely 11,12 , as it is readily applicable also to outputs from numerical atmospheric/climate models 13 . ?is approach

extracts sub-weekly ?uctuations of such meteorological variables as pressure, temperature or wind velocity locally

through digital high-pass ?ltering applied to their daily time series, and eddy activity is then measured locally

as their temporal variance or covariance11,12 . Regions of strong eddy activity thus measured are called "storm

tracks", and many studies have investigated the climatological seasonality of storm tracks and their interannual

or decadal variability based on Eulerian statistics 14 -16 . Another advantage of the Eulerian approach is its suit - ability to quantitative dynamical diagnoses, including the energetics based on the Lorenz energy cycle 16 -18 and the Eliassen-Palm (E-P) ?ux diagnosis for eddy-mean ?ow interaction 19-21 . ?e latter can, for example, illustrate

horizontal propagation of wave packets and associated translation of wave-activity pseudo-momentum. ?e

Eulerian statistics can also elucidate the dynamical distinction of an eddy-driven, subpolar westerly jet stream

from a stronger thermally driven subtropical jet stream22,23 .

?e aforementioned advantages of the Eulerian approach arise from treating cyclonic and anticyclonic eddies

together as deviations from the mean state, which in turn prevents us from targeting individual cyclonic and

anticyclonic eddies separately. Unlike the Lagrangian approach, the Eulerian statistics thus represent uni?ed

contributions from cyclones and anticyclones, which has limited our understanding of storm tracks and associ

-

ated eddy-mean ?ow interaction. ?is study is the ?rst to evaluate and reconstruct separate contributions from

both cyclonic and anticyclonic eddies onto Eulerian statistics, based on instantaneous identi?cation of cyclonic

and anticyclonic vortices. Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan.

Department

of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel. * email: okajima@

Vol:.(1234567890)

| (2021) 11:13202 | www.nature.com/scientificreports/

In the Northern Hemisphere, a cyclone (anticy-

clone) accompanies counterclockwise (clockwise) circulation. It is not dicult to identify its rotation center at

a near-surface level, where the background westerlies and associated pressure gradient are weak. In the upper

troposphere, however, identifying the rotation center is generally more dicult, because cyclonic (anticyclonic)

circulations oen appear as open pressure troughs (ridges) associated with a meandering westerly jet. An upper-

level geopotential height eld is therefore not suited for determining “centers", because of its strong meridional

gradient across the jet stream. A vorticity eld may be another possibility, but the center detection actually fails

due to strong shear vorticity along the westerly jet as schematically illustrated in Supplementary Fig.S1a.

To circumvent the aforementioned challenges in identifying pressure troughs and ridges (or cyclonic and

anticyclonic vortices, respectively) on both sides of a meandering jet (Supplementary Fig.S1b), a new method

developed here relies on curvature or curvature vorticity calculated from horizontal winds (see Methods). Sup

-

plementary Figs.S1c and S1d show snapshots of curvature elds in the upper and lower troposphere, respectively.

Positive and negative curvatures correspond well to upper-tropospheric pressure troughs and ridges, respectively,

and the corresponding near-surface cyclones/troughs and anticyclones/ridges as well. ese troughs and ridges

are represented with comparable magnitudes of curvature between the upper and lower troposphere, as an

advantage of the use of curvature over other measures (Supplementary Fig.S2). In fact, relative vorticity is less

eective in capturing those upper-tropospheric troughs and ridges (e.g., a ridge along ~ 165°E in Supplementary

Fig.S2), due to the shear vorticity included in the full relative vorticity (Supplementary Fig.S2c). In addition,

an upper-tropospheric cut-o low around [50°N, 175°W] coincides with a well-dened maximum of curvature

(Fig. S1c), which cannot be captured successfully by any of the other measures (Supplementary Fig.S2). Again,

this example demonstrates an advantage of using curvature, in addition to its straightforward physical mean

-

ing since its reciprocal is simply the radius of curvature and thus corresponds to the horizontal size of an eddy.

Climatological-mean probability of cyclonic vortices (with local positive curvature) is

shown in Fig.1 over the midwinter North Pacic. Since no threshold is set on local curvature to identify those

cyclonic vortices, the local residual represents the corresponding probability of anticyclonic vortices. In the

upper troposphere (Fig.1a), cyclonic vortices are more likely to be observed to the north of the westerly jet axis,

while anticyclonic vortices form more frequently to the south. A similar meridional contrast is observed across

the lower-tropospheric eddy-driven westerly jet (Fig.1b), but cyclonic vortices are oen observed also around

the jet axis. Contrastingly, the high probability of anticyclone vortices extending zonally around 20°

 25°N cor-

responds to the near-surface subtropical high-pressure belt. e lower-tropospheric statistics are overall consist

- ent with previous results from Lagrangian tracking 9 , 12 .

e new method allows us to evaluate contributions from cyclonic and anticyclonic vortices (or eddies)

separately to the Eulerian statistics, by accumulating instantaneous contributions only at grid points where

cyclonic or anticyclonic curvature is observed. As an example shown in Supplementary Fig.S3, curvature based

on instantaneous unltered winds is used only for determining domains of cyclonic and anticyclonic vortices, and

the separation of transient eddies from the background state has been achieved by the temporal ltering. Here,

no threshold is set for cyclonic and anticyclonic curvature in order not to miss any circulation on the fringes of

troughs and ridges. Figures2a-b show the climatological-mean contributions from cyclonic and anticyclonic

vortices, respectively, over the midwinter North Pacic to the variance of 300-hPa high-pass-ltered meridional

wind uctuations (V"V"300) as a measure of eddy activity. As in its total eld, contributions to V"V"300 from the

two polarities both maximize in the eastern North Pacic, although the anticyclonic contribution is slightly larger

and its maximum is located slightly downstream of its cyclonic counterpart. Distribution of 300-hPa poleward

ux of westerly momentum (U"V"300) by anticyclonic vortices is similar to but stronger than its cyclonic coun

-

terpart (Figs.2c-d). Both cyclonic and anticyclonic vortices yield the equatorward ux of momentum to the

Figure?1.

Probability of cyclonic and anticyclonic vortices. a-b, Climatological probability of cyclonic vortices

(colors; with positive curvature) at 300-hPa ( a) and 850-hPa (b) over the midwinter (24Jan) North Pacic. e

probability of anticyclonic vortices can be obtained as the local residual. Black contours indicate climatological-

mean U300 ( a) and U850 (b) (m/s).

Vol.:(0123456789)

| (2021) 11:13202 | www.nature.com/scientificreports/

north of ~ 40°N and the poleward ux to its south. ese converging uxes thus act to accelerate the westerlies

to the north and downstream of the prominent jet core around [32°N, 150°E]. e momentum ux diverges

northward out of the jet core region, characteristic of a thermally driven subtropical jet 22
,23 . Lower-tropospheric

poleward eddy heat ux (V"T"850) by cyclonic vortices (Fig.2e) is more than twice as strong as its anticyclonic

counterpart (Fig.2f), indicative of the prominent contribution from baroclinic cyclonic vortices to heat transport.

e threshold curvature for detecting cyclonic or anticyclonic vortices is not necessarily zero as in Fig.2.

For comparison, the corresponding climatological-mean probability of cyclonic and anticyclonic vortices is

shown in Supplementary Fig.S4, with the threshold curvature equivalent to the radius of curvature of 2500km.

As expected, the probability decreases substantially for the two polarities, but the spatial distribution overall

resembles that with the zero threshold. Unlike the case with the zero threshold, however, the probability of

anticyclonic vortices is not necessarily a mirror image of its cyclonic counterpart. Along the upper-tropospheric

westerly jet, for example, the probability for both cyclonic and anticyclonic vortices is very low. is is probably

because the prominent westerly jet, especially in its core region, is likely to ow steadily and barely meanders

to form vortices with small radii. Contributions to the Eulerian statistics are qualitatively similar to those with

zero curvature threshold, but with more striking distinctions between cyclonic and anticyclonic V"T"850 (Sup-

plementary Fig.S5), highlighting the dominant poleward heat ux concentrated around cyclone centers, as

inferred from a typical structure of extratropical cyclones 24
.

e aforementioned characteristics of the contribution from anticyclonic vortices to the Eulerian statistics

revealed with curvature, including comparable or even slightly stronger V"V"300, greater U"V"300, and weaker

Figure?2.

Separated contributions from cyclonic and anticyclonic vortices to Eulerian statistics. a-b,

Contributions to climatological-mean V"V"300

(m 2 /s 2 , colors) separately from cyclonic ( a) and anticyclonic

(b) vortices over the midwinter (24Jan) North Pacic. Contours denote climatological-mean total V"V"300

from all vortices. c-d , Same as in Figs.2a-b, respectively, but for U"V"300 (m 2 /s 2 , colors). Contours denote climatological-mean U300 (m/s). e-f , Same as in Figs.2a-b, respectively, but for heat ux V"T"850 (K m/s). Contours denote climatological-mean total V"T"850 (K m/s) from all vortices.

Vol:.(1234567890)

| (2021) 11:13202 | www.nature.com/scientificreports/

V"T"850 relative to their counterpart for cyclonic vortices, are not well represented if relative vorticity is used

in place of curvature (Supplementary Fig.S6). e discrepancies are attributable to shear vorticity, because

the decomposed Eulerian statistics based on shear vorticity exhibit consistent and even stronger biases (Sup

- plementary Fig.S7). e converging/diverging uxes of

heat and momentum by cyclonic and anticyclonic vortices imply their feedback forcing onto the climatologi

- cal-mean westerlies 25
, 26
. To quantify this, three-dimensional eddy momentum ux convergence (divergence) is

calculated as the westerly acceleration (deceleration) by eddies (see Methods for details), and its meridional sec

-

tions for the western North Pacic [150°E-180°] are shown in Figs.3a and b for cyclonic and anticyclonic eddies,

respectively. Consistently with Figs.2c-d, both cyclonic and anticyclonic vortices exert westerly deceleration

(ux divergence) around the midwinter Pacic jet core (at 200-hPa) and acceleration (ux convergence) to its

north through their poleward westerly momentum ux (Figs.3a-b), although the contribution from cyclonic

vortices is weaker. In fact, the westerly acceleration by cyclonic vortices occurring on the northern ank of the

jet exhibits a much shallower structure (Fig.3a). e near-surface westerly acceleration by cyclonic vortices

reaches nearly 3m/s a day, which is twice as strong as its anticyclonic counterpart and enough to replenish the

climatological low-level westerlies within 3days. is acceleration associated with the diverging upward and

poleward E-P ux is due to the enhanced low-level poleward heat ux and equatorward momentum ux by

cyclonic vortices. e latter diverges from the center of the Aleutian Low (AL), a semi-persistent surface oce

-

anic low-pressure system, as marked with zero zonal wind in Fig.3a. is diverging westerly momentum ux

(or converging E-P ux) yields strong lower-tropospheric westerly deceleration near the AL center, reecting

the tendency for poleward moving cyclones to be distorted meridionally under the strong cyclonic shear of the

westerlies 27
. e overall picture obtained from our analysis is that the poleward transport of westerly momentum

from the upper-tropospheric core of the climatological-mean jet driven by the Hadley Cell is contributed to

more by anticyclonic vortices. e transported westerly momentum is then transferred downward to maintain

the near-surface westerlies around 40°N along the southern fringe of the AL, which is mainly by cyclonic vorti

-

ces through their enhanced poleward heat transport. e near-surface westerly acceleration occurs also through

Figure?3.

Westerly wind acceleration by transient feedback forcing evaluated separately for cyclonic and

anticyclonic vortices. a-b, Meridional sections of climatological-mean net westerly wind acceleration or

deceleration as transient eddy feedback forcing (colors) by cyclonic vortices ( a) and anticyclonic vortices (b) for midwinter (24Jan). Quantities shown are zonally averaged for the western North Pacic [150°E  180°]. Black

contours denote climatological-mean westerly wind speed (every 10m/s, thick line for 0m/s). Vectors indicate

extended E-P ux20 associated with cyclonic and anticyclonic vortices. ( c-d ), Same as in a-b, respectively, but for the storm track over the midwinter North Atlantic [80°  50°W]. (e-f), Same as in a-b, respectively, but for the storm track over the midsummer South Indian Ocean [75°  105°E].

Vol.:(0123456789)

| (2021) 11:13202 | www.nature.com/scientificreports/

the distorted cyclonic vortices, which is most prominent in midwinter. e result is qualitatively similar when a

non-zero curvature threshold is used (Supplementary Fig.S8).

Our method to identify cyclonic and anticyclonic vortices can be applied to storm tracks over other ocean

basins as well. Figures3c-d show westerly acceleration exerted by cyclonic and anticyclonic vortices, respec-

tively, over the North Atlantic (averaged over 80°  50°W). In the lower troposphere, the westerly acceleration by

cyclonic vortices is much stronger, while it is slightly weaker in the upper troposphere than that by anticyclonic

vortices. Additionally, near-surface westerly deceleration by cyclonic vortices is striking along the southern

fringe (at

~ 60°N) of the semi-permanent Icelandic Low, especially in midwinter. ese characteristics are in

common with the North Pacic storm track. Figures3e-f show the corresponding westerly acceleration over

the summertime South Indian Ocean (averaged over 75°  105°E), where a distinct subpolar eddy-driven jet

forms at ~ 45°S. is situation resembles that over the summertime North Pacic. Lower-tropospheric westerly

acceleration by cyclonic vortices is much stronger than by anticyclonic vortices, while the contributions from

cyclonic and anticyclonic vortices are comparable in the upper troposphere. ese features are consistent with

the two Northern Hemispheric oceanic storm tracks. Over the summertime South Indian Ocean, poleward

westerly momentum ux in the upper troposphere from the subtropics into the midlatitude jet core is striking

for both cyclonic and anticyclonic vortices.

Furthermore, the decomposed Eulerian statistics

can be utilized for evaluating the cyclonic and anticyclonic contributions to the Lorenz energy cycle. e atmos

-

pheric energetics for the midwinter Northern Pacic (Fig.4) reveals that anticyclonic EKE accounts for ~ 45%

of the total EKE, indicating that anticyclones are almost as important as cyclones in the midlatitude energetics.

Reecting their baroclinic structure, the ratio of EAPE to EKE for cyclonic vortices is somewhat higher than

anticyclonic vortices.

e potential energy conversion (CP) to cyclonic vortices from the baroclinic background westerlies is greater

by ~ 60% compared to anticyclonic vortices, while cyclonic and anticyclonic vortices contribute comparably to the

barotropic kinetic energy conversion (CK) in maintaining the westerly jet stream. Both cyclonic and anticyclonic

vortices contribute positively to EAPE generation through diabatic heating (CQ). A striking feature in Fig.4 is the

predominant role of anticyclonic vortices in carrying eddy energy downstream (EF) out of the Pacic storm track.

Horizontal distributions of the CK and CP terms are overall similar between cyclonic and anticyclonic vor-

tices (Supplementary Fig.S9). Compared to cyclonic vortices, however, anticyclonic vortices give up slightly

more EKE to the background jet stream just to the south of its exit, while gaining less EKE in the jet core region.

Figure?4.

e Lorenz energetics separated into cyclonic and anticyclonic contributions. a-b, Climatological- mean energy budget averaged over the midwinter (24Jan) North Pacic [130°  130°W, 20°  65°N] for cyclonic

(a) and anticyclonic (b) vortices. CK denotes the barotropic energy conversion (or KE conversion) into the

background ow, CP the baroclinic energy conversion (or APE conversion) from the background ow, CQ the

APE generation through diabatic processes, ET energy transfer from EAPE to EKE, and EF the energy inow or

outow by energy uxes through lateral boundaries of the domain. EAPE and EKE are in unit of EJ (= 10 18 J), while CK, CP, ET and EF in unit of TW (= 10 12 W). All the terms are integrated vertically from the surface to

100-hPa. e gure was created with Inkscape v1.0.1 (

https:// www. inksc ape. org).

Vol:.(1234567890)

| (2021) 11:13202 | www.nature.com/scientificreports/

us, the net CK to the background westerlies from anticyclonic eddies is slightly larger especially in the upper

troposphere (Supplementary Figs.S10a-b). e cyclonic CP is much stronger especially over the western North

Pacic (Supplementary Figs.S9c-d), where cyclonic development is promoted along a prominent oceanic frontal

zone that acts to reinforce the near-surface baroclinicity in addition to abundant moisture supply from the warm

Kuroshio Extension

23
. e dierences between the cyclonic and anticyclonic CP are found mainly in the lower

and mid-troposphere (Supplementary Figs.S10c-d). e anticyclonic CP is concentrated in the upper tropo

-

sphere and actually it is comparable to the cyclonic CP when integrated only in the mid- and upper troposphere

(Supplementary Fig.S11). ese energetic features are overall consistent with the results in Fig.3.

In this study, the conventional Eulerian statistics and Lorenz energy cycle are decomposed into the contributions

from cyclonic and anticyclonic vortices based on the separate identication of these two types of vortices. is

gives new insights for understanding of storm track dynamics and eddy-mean ow interaction, especially the

distinct roles of cyclonic and anticyclonic vortices in maintaining the mean westerlies, in addition to the atmos

-

pheric energetics. e novel approach used here allows us to expand the knowledge about storm tracks obtained

thus far based solely on either the Eulerian statistics or Lagrangian tracking. e latter has been applied almost

exclusively to near-surface cyclones, but our approach suggests that roles of anticyclones should not be over-

looked. Moreover, our approach allows separating the atmospheric energetics into their cyclonic and anticyclonic

contributions, pointing to the important role of anticyclones in the overall energy budget and energy conversion.

Our new method can lead to identication of distinct roles, if any, of cyclonic and anticyclonic eddies in caus

- ing the counterintuitive observed midwinter suppression of the North Pacic storm track activity 14 ,15 . Likewise, dynamics of the annular modes over the Northern and Southern Hemispheres 28
, the baroclinic annular mode 29
, and blocking highs 30
-32 can also be addressed through our new unied approach between the Lagrangian and

Eulerian perspectives. e same will be the case for output of climate models, including future climate projec-

tions and large ensemble simulations, in which changes in positions and activity of storm tracks have been

intensively studied 33
-36 .

Previous studies have examined the observed

trend 37
and future change 38
-40 in atmospheric energetics based

on the Lorenz energy cycle. ese studies helped understand climate change from an energetic point of view,

into which the present study can give a new insight. Furthermore, the separation of cyclonic and anticyclonic

contributions to the atmospheric energy cycle can be useful for the validation of the climate model simulations,

providing us with a more phenomenological way to interpret and constituting another constraint for the models.

Recently, the eect of global warming on wind power generation, which ultimately determines the amount of

wind energy that can be extracted for power generation 41
, has been investigated in the framework of atmospheric energetics 42

. Our new approach has the potential to delineate separate roles of cyclones and anticyclones in the

origin of near-surface wind energy. We analyzed 6-hourly global elds of atmospheric variables, including SLP and geo-

potential height, air temperature, wind velocity, and diabatic heating rates in the pressure coordinates, obtained

from the Japanese 55-year reanalysis (JRA-55) by the Japan Meteorological Agency (JMA) 43
, 44
for the period

1958/59-2016/17. e JRA-55 has been constructed through a four-dimensional variational data assimilation

(4D-Var) system with TL319 horizontal resolution (equivalent to 55-km) and 60 vertical levels up to 0.1-hPa.

Variables on selected pressure levels are available on a 1.25° × 1.25° grid system. At a particular grid, uctuations of a given variable with syn-

optic-scale transient eddies whose period is shorter than about a week have been extracted from the 6-hourly

atmospheric reanalysis as its deviations from their low-pass-ltered elds with an 8-day cuto Lanczos lter (in

this paper, primes denote local deviations from the climatological mean). Local activity of those transient eddies

or their uxes is evaluated as the variance based on the sub-weekly uctuations of meridional velocity or the

covariance representing poleward eddy heat ux. Regions of high eddy activity corresponds to “storm tracks",

along which transient eddies recurrently develop. Climatological-mean elds plotted in Figs.2 and 3 for a given

midwinter day are calculated aer applying a 31-day running mean to daily climatology. Vorticity can be decomposed locally into shear and cur- vature terms as follows 45
- 47

where V denotes scalar wind speed, n the direction perpendicular to the ow, and Rs the radius of curvature.

e rst and second terms of the RHS in Eq.(1) represent shear vorticity and curvature vorticity, respectively,

which can be calculated as(1) ∂σ z t  z   (2)=1? 1? ?= σ ? ∂ = = ((( ? =( ∂ ( ? +( ∂ ( ? +((( ? -

Vol.:(0123456789)

| (2021) 11:13202 | www.nature.com/scientificreports/

where u and v denote local zonal and meridional wind velocities, respectively, and subscripts x and y partial

derivatives in the zonal and meridional directions, respectively. e curvature, dened as can be derived from the denition of curvature of a two-dimensional curve implicitly represented by ∂z=t σ 1g;

e curvature or curvature vorticity enables us to circumvent the diculties in determining areas of cyclonic and

anticyclonic circulations, because it is free from shear vorticity and thus extracts vortex circulation with a certain

radius. A similar quantity, curvature vorticity multiplied by a scalar wind speed (named Eulerian Centripetal

Acceleration or ECA), was utilized to track 500-hPa mobile pressure troughs 45
,48 . As shown in Supplementary

Fig.S2e, ECA well captures centers of upper-tropospheric troughs along a strong westerly jet, which was the

purpose of contriving ECA 45
. Meanwhile, ECA is less eective in representing the center of an upper-tropospheric

cut-o low than the curvature (Supplementary Fig.S1c). Another aspect of ECA is a distinct dierence in its

amplitude between the upper and lower troposphere (Supplementary Figs.S2e and S2f.), which is due to the

direct contribution of squared wind speed. At this point, curvature is suitable for identifying three-dimensional

cyclonic and anticyclonic vortices and evaluating those contributions to the atmospheric energy cycle, whereas

ECA is compatible with the identication of centers of troughs at a given mid- or upper-tropospheric level. In

this study, curvature is weakly smoothed by applying a 9-point horizontal smoothing (weight is 0.5 next to the

center point and 0.3 at corners) twice when used for determining the direction of local circulation (cyclonic or

anticyclonic).

In addition to the potential application of curvature to meteorological and climatic phenomena including

cut-o lows, the decomposition of vorticity into the curvature and shear terms can be useful for other elds of

geoscience, because curvature is calculated purely locally with no laborious procedures required. For example,

we can distinguish and identify ocean eddies and jets along the western boundary currents, or determine the

boundary of a given warm/cold core eddy. In the case of the meandering Kuroshio Extension as in Supplemen-

tary Fig.S12a, relative vorticity includes mixed contributions from the vortex and shear terms (Supplementary

Fig. S12b). e curvature term better depicts eddies (Supplementary Fig.S12c), while the shear term helps us

identify oceanic jets (Supplementary Fig.S12d). For example, a mesoscale cyclonic eddy associated with the

meandering Kuroshio is better resolved as an isolated vorticity maximum around [32°N, 139°E], whereas shear

vorticity depicts more continuous bands of positive and negative values than relative vorticity, representing the

meandering Kuroshio current and its eastward Extension. is decomposition can therefore be helpful for elu-

cidating dynamical processes involved in the maintenance and variability of the oceanic jet under the possible

feedback forcing from eddies. e identication of ocean eddies through curvature and curvature vorticity based

on horizontal ow elds may thus be more straightforward than, for example, the commonly used Okubo-Weiss

(OW) parameter 49
,50 or identication based on sea surface height 51
.

It may be informative to show the relationship between the curvature utilized in this study and the OW

parameter, which is dened as

e last equality holds for the case of horizontally non-divergent ow. e last term is related to Gaussian

curvature of three-dimensional surface, since for a given surface ?σ= p ??? R , Gaussian curvature is dened as e numerator is clearly one fourth of the OW parameter where 0?x,y ? represents the streamfunction.

e curvature used in this study focuses on a two-dimensional isocurve, while the OW parameter focuses on

a curved surface.

One should be cautious in calculating Eulerian statistics based on the vorticity decomposition. In the present

study, for example, V"V" is calculated from a high-pass-ltered eld of total (not decomposed) meridional wind

as shown in Supplementary Fig.S3. It might be possible to calculate eddy variance and covariance from decom

- posed velocities such as v=v C +v A +v S , where subscripts “C", “A", and “S" denote velocities derived from positive and negative curvature vorticity and shear vorticity terms, respectively (e.g., v C = ∂ x ? - ?  2 ? - 1 ζ C ? ; ζ C

denotes positive curvature vorticity). However, those second (or higher) order statistics can have non-negligible

contributions from “cross terms" in such a way that V ? V ? =V ? C V ? C V ? A V ? A V ? S V ? S V ? C V ? A V ? A V ? S V ? S V ? C ,

and the correlation coecients between the decomposed velocity components may not necessarily be small. (3)

V R S = 1 V 2 ? - uvu x +u 2 v x -v 2 u y +uvv y ? (4) κ 2 ≡ 1 R S  1 V 3 ? - uvu x +u 2 v x -v 2 u y +uvv y ? (5) κ 2 ≡ ? ?????ψ xx ψ xy ψ x ψ yx ψ yy ψ y ψ x ψ y 0 ??????  ψ 2x +ψ 2y ? 3 /2 (6)W= ? v  +u  ? 2 + ? u  -v  ? 2 - ? v  -u  ? 2 =4 ? v    -u 2 x ? (7) κ 3 ≡ψ xx ψ yy -ψ 2 xy ?

1+ψ

2x +ψ 2y ?

Vol:.(1234567890)

| (2021) 11:13202 | www.nature.com/scientificreports/

Whether such second-order statistics are dominated by contributions from the decomposed vorticity terms and

those from the “cross terms" are negligible should be veried in future studies. Feedback forcing exerted on quasi-steady background ow by

eddies migrating along a storm track is estimated locally as a geopotential height tendency that could be induced

through uxes of heat and vorticity by transient eddies 25
, 52
, 53
, as follows:

In Eq.(8), an overbar denotes a variable for the background ow, which corresponds to the climatological-

mean state in our practice. e feedback forcing by high-frequency transient eddies was estimated through

the eddy uxes as evaluated locally from 6-hourly uctuations through the temporal high-pass ltering. High-

frequency transients are always exerting feedback forcing onto the background state in which they are embedded.

In the climatological-mean state their feedback forcing must therefore be balanced with other processes. Eddy

feedback forcing as acceleration (or deceleration) of westerly winds is estimated by calculating westerly wind

tendency from the geopotential tendency by assuming geostrophic balance. We utilized daily zonal and meridional velocities of ocean currents over the western North Pacic obtained from the FORA-WNP30 reanalysis 54
by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) and Meteorological Research Institute (MRI). e FORA-WNP30 was

produced by the MRI Multivariate Ocean Variational Estimation system version of 4-dimensional variational

method (MOVE-4DVAR 55
), and the data assimilation system developed by the JMA/MRI, which uses an eddy- resolving ocean model for the western North Pacic. Its horizontal resolution is 1/10° × 1/10° with 54 vertical levels (0

~ 6300m depth). To focus on the structure of oceanic jets and mesoscale eddies, velocity elds have

been smoothed by performing a 9-point horizontal smoothing (with weights of 0.5 next to the center point and

0.3 at corners) 15 times for the snapshots plotted in Supplementary Fig.S12.

e formulation of atmospheric energetics here is follow- ing previous studies 56
, 57
. Climatological-mean state is considered as a background state for high-pass-ltered uctuations. All the terms are three-dimensionally integrated over the North Pacic domain [130°E  130°W,

20°

 65°N] and between specied vertical levels. e residue corresponds mainly to the dissipation of EKE with

contributions from interactions between high-frequency eddies and low-frequency variabilities. e JRA-55 atmospheric reanalysis is available online in https:// jra. kishou. go. jp/ JRA- 55/
index_ en. html. e FORA-WNP30 oceanic reanalysis is available online in http:// www. godac. jamst ec. go. jp/ fora/e/ index. html. Received: 23 December 2020; Accepted: 10 June 2021

1. Hurrell, J. W. Transient eddy forcing of the rotational ow during northern winter. J. Atmos. Sci. 52(12), 2286-2301 (1995).

2. Rogers, J. C. North Atlantic storm track variability and its association to the North Atlantic Oscillation and climate variability of

northern Europe.

J. Clim.

10(7), 1635-1647 (1997).

3. Loikith, P. C. & Broccoli, A. J. Characteristics of observed atmospheric circulation patterns associated with temperature extremes

over North America.

J. Clim.

25(20), 7266-7281 (2012).

4. Pfahl, S. & Wernli, H. Quantifying the relevance of cyclones for precipitation extremes. J. Clim. 25(19), 6770-6780 (2012).

5. Catto, J. L. & Pfahl, S. e importance of fronts for extreme precipitation. J. Geophys. Res. Atmos. 118(19), 791-801 (2013).

6. Pfahl, S., Madonna, E., Boettcher, M., Joos, H. & Wernli, H. Warm conveyor belts in the ERA-Interim dataset (1979-2010) Part

II: Moisture origin and relevance for precipitation.

J. Clim. 27(1), 27-40 (2014).

7. Hinman, R. Eclectic Physical Geography. (American Book Company, Cincinnati, 1888).

8. Murray, R. J. & Simmonds, I. A numerical scheme for tracking cyclone centres from digital data Part II: Application to January

and July general circulation model simulations.

Aust. Meteorol. Mag. 39(3), 167-180 (1991).

9. Hoskins, B. J. & Hodges, K. I. New perspectives on the Northern Hemisphere winter storm tracks. J. Atmos. Sci. 59(6), 1041-1061

(2002).

10. Ulbrich, U., Leckebusch, G. C. & Pinto, J. G. Extra-tropical cyclones in the present and future climate: a review. ?eor. Appl. Cli-

matol. 96(1-2), 117-131 (2009).

11. Blackmon, M. L., Wallace, J. M., Lau, N. C. & Mullen, S. L. An observational study of the Northern Hemisphere wintertime circula-

tion. J. Atmos. Sci. 34(7), 1040-1053 (1977).

12. Wallace, J. M., Lim, G. H. & Blackmon, M. L. Relationship between cyclone tracks, anticyclone tracks and baroclinic waveguides.

J. Atmos. Sci.

45(3), 439-462 (1988).

13. Flato, G. etal. Evaluation of climate models. Climate change 2013: ?e Physical Science Basis. Contribution of Working Group I

to the Fi?h Assessment Report of the Intergovernmental Panel on Climate Change (eds Stocker, T. F. etal.) 7 741-866 (Cambridge

Univ. Press, 2013).

14. Nakamura, H. Midwinter suppression of baroclinic wave activity in the Pacic. J. Atmos. Sci. 49(17), 1629-1642 (1992).

∂z ∂=1g? ? 2 +f 2 ∂ p?

1σ∂ p??

- 1 · ( (  f?· ? V ? ζ ? ? f 2 ∂ p ( ( -? ·?V ? θ ? ? - ∂¯? p ) )) ) (8)σ=-∂ ¯  p R ? 00 ? R/c p

Vol.:(0123456789)

| (2021) 11:13202 | www.nature.com/scientificreports/

15. Nakamura, H., Izumi, T. & Sampe, T. Interannual and decadal modulations recently observed in the Pacic storm track activity

and East Asian winter monsoon.

J. Clim.

15(14), 1855-1874 (2002). 16. Chang, E. K., Lee, S. & Swanson, K. L. Storm track dynamics. J. Clim. 15(16), 2163-2183 (2002).

17. Lorenz, E. N. Available potential energy and the maintenance of the general circulation. Tellus 7(2), 157-167 (1955).

18. Orlanski, I. & Katzfey, J. e life cycle of a cyclone wave in the Southern Hemisphere Part I: Eddy energy budget. J. Atmos. Sci.

48
(17), 1972-1998 (1991).

19. Hoskins, B. J., James, I. N. & White, G. H. e shape, propagation and mean-ow interaction of large-scale weather systems. J.

Atmos. Sci.

40, 1595-1612 (1983).

20. Trenberth, K. E. An assessment of the impact of transient eddies on the zonal ow during a blocking episode using localized

Eliassen-Palm ux diagnostics.

J. Atmos. Sci.

43, 2070-2087 (1986).

21. Plumb, R. A. ree-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of

the time-mean ow.

J. Atmos. Sci. 43(16), 1657-1678 (1986).

22. Lee, S. & Kim, H. K. e dynamical relationship between subtropical and eddy-driven jets. J. Atmos. Sci. 60(12), 1490-1503 (2003).

23. Nakamura, H., Sampe, T., Tanimoto, Y. & Shimpo, A. Observed associations among storm tracks, jet streams, and midlatitude

oceanic fronts Earth Climate: e Ocean-Atmosphere Interaction.

Geophys. Monogr. 147, 329-345 (2004).

24. Wang, C. C. & Rogers, J. C. A composite study of explosive cyclogenesis in dierent sectors of the North Atlantic Part I: Cyclone

structure and evolution.

Mon. Weather Rev. 129(6), 1481-1499 (2001).

25. Lau, N. C. & Holopainen, E. O. Transient eddy forcing of the time-mean ow as identied by geopotential tendencies. J. Atmos.

Sci. 41, 313-328 (1984).

26. Nakamura, H., Miyasaka, T., Kosaka, Y., Takaya, K. & Honda, M. Northern Hemisphere extratropical tropospheric planetary waves

and their low-frequency variability: eir vertical structure and interaction with transient eddies and surface thermal contrasts.

Climate Dyn Why Does Climate Vary Geophys. Monogr. 189, 149-179 (2010).

27. Tamarin, T. & Kaspi, Y. e poleward motion of extratropical cyclones from a potential vorticity tendency analysis. J. Atmos. Sci.

73
(4), 1687-1707 (2016).

28. ompson, D. W. & Wallace, J. M. Annular modes in the extratropical circulation Part I: Month-to-month variability. J. Clim.

13 (5), 1000-1016 (2000).

29. ompson, D. W. & Woodworth, J. D. Barotropic and baroclinic annular variability in the Southern Hemisphere. J. Atmos. Sci.

71
(4), 1480-1493 (2014).

30. Nakamura, H. & Wallace, J. M. Synoptic behavior of baroclinic eddies during the blocking onset. Mon. Weather Rev. 121(7),

1892-1903 (1993).

31. Nakamura, H., Nakamura, M. & Anderson, J. L. e role of high-and low-frequency dynamics in blocking formation. Mon. Weather

Rev. 125(9), 2074-2093 (1997).

32. Yamazaki, A. & Itoh, H. Vortex-vortex interactions for the maintenance of blocking Part I: e selective absorption mechanism

and a case study.

J. Atmos. Sci. 70, 725-742 (2013).

33. Yin, J. H. A consistent poleward shi of the storm tracks in simulations of 21st century climate. Geophys. Res. Lett. 32(18), L18701

(2005).

34. Ulbrich, U. et al. Changing Northern Hemisphere storm tracks in an ensemble of IPCC climate change simulations. J. Clim. 21(8),

1669-1679 (2008).

35. Chang, E. K., Guo, Y. & Xia, X. CMIP5 multimodel ensemble projection of storm track change under global warming. J. Geophys.

Res. Atmos.

117, D23118 (2012).

36. Shaw, T. A. et al. Storm track processes and the opposing inuences of climate change. Nat. Geosci. 9(9), 656-664 (2016).

37.

Pan, Y. et al. Earth"s changing global atmospheric energy cycle in response to climate change. Nat. Commun. 8(1), 1-8 (2017).

38. Hernández-Deckers, D. & von Storch, J. S. Energetics responses to increases in greenhouse gas concentration. J. Clim. 23(14),

3874-3887 (2010).

39. Hernández-Deckers, D. & von Storch, J. S. e energetics response to a warmer climate: relative contributions from the transient

and stationary eddies.

Earth Sys. Dyn. 2, 105-120 (2011).

40. Veiga, J. A. P., & Ambrizzi, T. A global and hemispherical analysis of the Lorenz energetics based on the representative concentra-

tion pathways used in CMIP5.

Adv. Meteorol. 2013, 485047 (2013).

41. Gustavson, M. R. Limits to wind power utilization. Science 204(4388), 13-17 (1979).

42. Huang, J. & McElroy, M. B. A 32-year perspective on the origin of wind energy in a warming climate. Renew. Energy 77, 482-492

(2015). 43.

Kobayashi, S. et al. e JRA-55 Reanalysis: General specications and basic characteristics. J. Meteor. Soc. Japan 93, 5-48 (2015).

44. Harada, Y. et al. e JRA-55 Reanalysis: Representation of atmospheric circulation and climate variability. J. Meteor. Soc. Japan

94
, 269-302 (2016).

45. Lefevre, R. J. & Nielsen-Gammon, J. W. An objective climatology of mobile troughs in the Northern Hemisphere. Tellus A 47(5),

638-655 (1995).

46. Holton, J. R. An introduction to dynamic meteorology 4th edn. (Academic Press, 2004).

47. Viúdez, Á. & Haney, R. L. On the shear and curvature vorticity equations. J. Atmos. Sci. 53(22), 3384-3394 (1996).

48. Piva, E. D., Gan, M. A. & Rao, V. B. An objective study of 500-hPa moving troughs in the Southern Hemisphere. Mon. Weather

Rev. 136(6), 2186-2200 (2008).

49. Okubo, A. Horizontal dispersion of oatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res.

Oceanogr. Abstr. 17(3), 445-454 (1970).

50. Weiss, J. e dynamics of enstrophy transfer in two-dimensional hydrodynamics. Phys. D 48(2-3), 273-294 (1991).

51. Chelton, D. B., Schlax, M. G. & Samelson, R. M. Global observations of nonlinear mesoscale eddies. Progr. Oceanogr. 91(2), 167-216

(2011).

52. Nishii, K., Nakamura, H. & Miyasaka, T. Modulations in the planetary wave eld induced by upward propagating Rossby wave

packets prior to stratospheric sudden warming events: A case study.

Q. J. R. Meteorol. Soc.

135(638), 39-52 (2009).

53. Okajima, S. et al. Mechanisms for the maintenance of the wintertime basin-scale atmospheric response to decadal SST variability

in the North Pacic subarctic frontal zone.

J. Clim.

31(1), 297-315 (2018).

54. Usui, N., Fujii, Y., Sakamoto, K. & Kamachi, M. Development of a four-dimensional variational assimilation system for coastal

data assimilation around Japan.

Mon. Weather Rev.

143(10), 3874-3892 (2015).

55. Usui, N. et al. Four-dimensional Variational Ocean Reanalysis: A 30-year high-resolution dataset in the western North Pacic

(FORA-WNP30). J. Oceanogr. 73, 205-233 (2017).

56. Kosaka, Y., Nakamura, H., Watanabe, M. & Kimoto, M. Analysis on the dynamics of a wave-like teleconnection pattern along the

summertime Asian jet based on a reanalysis dataset and climate model simulations.

J. Meteorol. Soc. Japan

87(3), 561-580 (2009).

57. Tanaka, S., Nishii, K. & Nakamura, H. Vertical structure and energetics of the western Pacic teleconnection pattern. J. Clim.

29
(18), 6597-6616 (2016).

Vol:.(1234567890)

| (2021) 11:13202 | www.nature.com/scientificreports/

e authors are grateful to the two anonymous reviewers for their sound criticism and constructive comments

on the earlier versions of this paper. is study is supported in part by the Japanese Ministry of Education,

Culture, Sports, Science and Technology (MEXT) through the Arctic Challenge for Sustainability II (ArCS-

II; JPMXD1420318865), by the Japan Science and Technology Agency through COI-NEXT JPMJPF2013, by the Japanese Ministry of Environment through Environment Research and Technology Development Fund

JMEERF20192004, and by the Japan Society for the Promotion of Science (JSPS) through Grants-in-Aid for

Scientic Research JP18H01278, JP19H05702 (on Innovative Areas 6102) and 20H01970. Y.K. acknowledges

support from the JSPS Invitational Fellowship for Research in Japan that supported a sabbatical at the University

of Tokyo and ignited this collaboration, for support from the Research Center for Advanced Technology and

Science at the University of Tokyo and the Israeli Science Foundation (grant 996/20).

S. O. designed the research at the suggestion of H.N. and performed the analyses. S. O. and H.N. wrote the

manuscript with discussion and feedback from Y. K. All authors reviewed the manuscript. e authors declare no competing interests.

Supplementary Information

e online version contains supplementary material available at https:// doi. org/ 10. 1038/
s41598- 021-

92548-7

.

Correspondence

and requests for materials should be addressed to S.O.

Reprints and permissions information

is available at www.nature.com/reprints .

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional aliations.

Open Access

is article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or

format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the

Creative Commons licence, and indicate if changes were made. e images or other third party material in this

article are included in the article"s Creative Commons licence, unless indicated otherwise in a credit line to the

material. If material is not included in the article"s Creative Commons licence and your intended use is not

permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from

the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.

© e Author(s) 2021